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- Let X1, X2,... , Xn be independent Exp(A) random variables. Let Y = X(1)min{X1, X2, ... , Xn}. Show that Y follows Exp(nA) dis- tribution. Hint: Find the pdf of YLet X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Let X1, X2, X3 be independent Exp()-distributed random vairables. Determine the pdf of X(1)X(3)
- 3. Let X and Y be two continuous random variables with joint PDF of + 03. Let X and Y be continuous random variables with joint PDF (3x 0s ysxs1 f(x, y) = {* otherwise Determine the correlation of variables X and Y.Example 2.17 Let X be a continuous type random variable with PDF given as 1 = (x)f 27 Let Y be another random variable such that Y = X². Find the PDF of Y.Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; isSuppose Y1 and Y2 are random variables with joint pdf (6(1 — у2), 0, 0 < y1 < y2 fv, otherwise Y1 Let U1 and U2 = Y,. Use the transformation technique to show that U, follows a uniform Y2 distribution from 0 to 1.9. (25 points) Let X and Y be a random variables of the continuous type having the joint pdf f(x, y) = 8xy, %3D (a) [10 points] Find fa(1) and fy(y). (b) [15 points] Find Cov(X,Y) and correlation coefficient.We have a random variable X and Y that jave the joint pdf f(x) = {1 0<x<1, 0<y<1} {0 otherwise} If U = Y-X2 , what is the support for the random variable U? What would fu(u) and Fu(u) be? Say U = Y/X, what is the support for the random variable U? What would fu(u) and Fu(u) be?4 Assume the PDFS of the two independent random variables X and Y are, 1, 0Let the joint pdf of random variables X,Y be fx,y (x, y) = a(x + y)e-2-Y, for all æ > 0, y 2 0. Find the conditional pdf Tylx (y|x) = &x2) fx(x)SEE MORE QUESTIONSRecommended textbooks for youElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
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